Spectral Properties and Geometric Interpretation of R-Filters

LENG Tuo

Volume 30 Issue 1

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(1): 109-119

LENG Tuo. Spectral Properties and Geometric Interpretation of R-Filters[J]. Applied Mathematics and Mechanics, 2009, 30(1): 109-119.

Citation:

LENG Tuo. Spectral Properties and Geometric Interpretation of R-Filters[J]. Applied Mathematics and Mechanics, 2009, 30(1): 109-119.

Citation:

LENG Tuo. Spectral Properties and Geometric Interpretation of R-Filters[J]. Applied Mathematics and Mechanics, 2009, 30(1): 109-119.

PDF( 402 KB)

Spectral Properties and Geometric Interpretation of R-Filters

LENG Tuo

Laboratory for Automated Reasoning and Programming, Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, P. R. China

Received Date: 2008-05-03
Rev Recd Date: 2008-12-01
Publish Date: 2009-01-15

Abstract

Abstract

Applying the Fourier analysis, the spectral properties of the R-filters are studied. Further, it was proved that R-filters is a generalization of least squares polynomial adjustment. And the geometric interpretation of R-filters was given.
- R-filter,
- HP-filter,
- spectral property,
- Fourier analysis,
- Hess-matrix,
- operator theory

FullText(HTML)

References(10)

References

[1]	Hodrick R J，Prescott E C, Postwar U S. Business cycles:an empirical investigation[J].Journal of Money,Credit,and Banking,1997,29(1):1-16. doi: 10.2307/2953682
[2]	Araujo Fabio, Areosa Marta Baltar Moreira, Neto Jose Alvaro Rodrigues.R-filters:a Hodrick-Prescott filter generalization[R]. Working Paper Series, 69,2003, 1-37.
[3]	Ehlgen Jürgen.Distortionary effects of the optimal Hodrick-Prescott filter[J]. Economic Letters,1998, 61(3):345-349. doi: 10.1016/S0165-1765(98)00190-6
[4]	Razaak W. The Hodrick-Prescott technique:a smooler versus a filter. an application to New Zealand GDP[J].Economic Letters,1997,57(2):163-168.
[5]	Cogly Timothy, Nason James M. Effects of the Hodrick-Prescott filter on trend and difference stationary time series. implication for business cycle research[J].Journal of Economic Dynamics and Control,1995,19(1/2):253-278. doi: 10.1016/0165-1889(93)00781-X
[6]	King Robert G, Rebelo Sergio T.Low frequency filtering and real business cycles[J]. Journal of Economic Dynamics and Control,1993,17:207-231.
[7]	Reeves J J, Blyth C A, Small J P.The Hodrick-Prescott filter, a generalization,and a new procedure for extracting an empirical cycle from series[J]. Studies in Nonlinear Dynamics and Economics,2000,4(1):1-16. doi: 10.1162/108118200569153
[8]	Baxter M, King Robert G. Measure business cycles approximate band-pass filters for economic time series[J].The Review of Economics and Statistics,1999,81(4):575-593. doi: 10.1162/003465399558454
[9]	Apel Mikael, Hansen Jan, Lindberg Hans. Potential output and output gap[J].Quarterly Review of the Bank of Sweden, 1996,3:24-35.
[10]	Horn R, Johnson C R.Martrix Analysis[M].New York:Cambridge University Press, 1985.